OFFSET
1,1
COMMENTS
These rational numbers represent a FRACTRAN program that generates the decimal expansion of Pi (A000796).
Conway proves that, when this program is started at 2^k (with k >= 0), the next power of 2 to appear is 2^Pi_d(k), where Pi_d(0) = 3 and, for k >= 1, Pi_d(k) is the k-th digit after the point in the decimal expansion of Pi.
LINKS
J. H. Conway, "FRACTRAN: A Simple Universal Programming Language for Arithmetic", in J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, American Mathematical Society, 2010, p. 249, and in T. M. Cover and B. Gopinath, eds, Open Problems in Communication and Computation, Springer, New York, NY, 1987, pp. 4-26.
Wikipedia, FRACTRAN.
CROSSREFS
KEYWORD
nonn,frac,fini,full
AUTHOR
Paolo Xausa, Jan 05 2022
STATUS
approved